I've used Isopropol Alcohol and some q-tips with some success. Also, when done, I've coated the exposed screws, carefully, with clear nail polish. You can't tell there was ever an issue.

Just be careful with the alcohol. If it gets on stickers or paint it will harm them. Might be better to just use WD-40. Taco Bell hot sauce maybe? That works well for cleaning up coins that I've found in the heating vents of my house.

I haven't tried any rust remover personally but I remember someone at Shoryuken.com being able to restore an old and badly rusted arcade joystick control panel using a green gel rust remover (I believe it was Bull Frog Rust Remover)
There's also Evapo-Rust and Rust Release SuperGel but again I haven't tried any of these personally (but I guess you can google these products to gather some feedback)

I tried WD-40, that stuff does not work too well. It helps to prevent rust, but to remove rust, it takes a lot of rubbing, and I mean A LOT. I also tried soaking screws in Coca Cola, but they turned black.

Baking Soda is the way to go. The way it works is like sandpaper, just that it is a lot milder than sandpaper that it would not deform your screw, or scratch your plastic in case you can't unscrew it.

i went to ebay and found an old junk lot i bought for about $14 that included plenty of screws of every size. you just have to take all of the junkers apart and seperate the screws by size into little containers.